Question
Solve the following equations. Check your result in case.
$\frac{1}{2}\text{x}-3=5+\frac{1}{3}\text{x}$
$\frac{1}{2}\text{x}-3=5+\frac{1}{3}\text{x}$
✓
Answer
$\frac{1}{2}\text{x}-3=5+\frac{1}{3}\text{x}$
$\Rightarrow\frac{1}{2}\text{x}-\frac{1}{3}\text{x}=5+3$ (By transposing)
$\Rightarrow\frac{3\text{x}-2\text{x}}{6}=8$
$\Rightarrow\frac{\text{x}}{6}=8$
$\Rightarrow\text{x}=8\times6$
$\Rightarrow\text{x}=48$
$\therefore\text{x}=48$
Check:
$\text{L.H.S}=\frac{1}{2}\text{x}-3=\frac{1}{2}\times48-3$
$=24-3=21$
$\text{R.H.S.}=5+\frac{1}{3}\text{x}$
$=5+\frac{1}{3}\times48=5+16=21$
$\text{L.H.S.}=\text{R.H.S.}$
Hence $\text{x}=48$
$\Rightarrow\frac{1}{2}\text{x}-\frac{1}{3}\text{x}=5+3$ (By transposing)
$\Rightarrow\frac{3\text{x}-2\text{x}}{6}=8$
$\Rightarrow\frac{\text{x}}{6}=8$
$\Rightarrow\text{x}=8\times6$
$\Rightarrow\text{x}=48$
$\therefore\text{x}=48$
Check:
$\text{L.H.S}=\frac{1}{2}\text{x}-3=\frac{1}{2}\times48-3$
$=24-3=21$
$\text{R.H.S.}=5+\frac{1}{3}\text{x}$
$=5+\frac{1}{3}\times48=5+16=21$
$\text{L.H.S.}=\text{R.H.S.}$
Hence $\text{x}=48$
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